BRUSSELS — A major leap in the European Union’s digital policy and a new defense department will be two of the bloc’s top priorities for the next five years, as the new leadership and organization of its 32,000-strong executive arm was unveiled on Tuesday.

The incoming president of that executive arm, the European Commission, is Germany’s Ursula von der Leyen. She announced her team of commissioners, one from each of the 28 member states except for Britain, which is on its way out. The lineup was the commission’s most gender-balanced yet, with 12 women plus Ms. von der Leyen at the helm, alongside 14 men.

Here are the most interesting, controversial and consequential things you need to know about how the European Union will be run in the next five years.

Margrethe Vestager will be Europe’s queen of digital.

Opposed by big tech companies, especially in the United States, for opening battle lines against firms Google, Facebook and others, Margrethe Vestager has been a political and punchy European commissioner for competition for the past five years.

But instead of moving on or becoming less important under the new boss, Ms. Vestager, from Denmark, will become even more powerful.

The reorganization Ms. von der Leyen presented on Tuesday places Ms. Vestager in charge of everything digital. Her new portfolio will include measures to unify the European Union digital market, bolster cybersecurity and finance innovation. She will also continue to oversee antitrust matters, together with the commission’s army of competition lawyers.

It’s a promotion, and an unusual merger of jobs, that will involve Ms. Vestager looking at several sides of technology: serving consumers and overseeing competition, while also enforcing Europe’s strict privacy and data security rules.

There’ll be a defense union, but not a military alliance.

Ms. von der Leyen most recently served as Germany’s defense minister, and it shows. In her new commission, she is creating a new “directorate general,” or branch of administration, to deal with harmonizing the development of weapons and defense systems in the European Union.

The portfolio will be led by France’s Sylvie Goulard, and is significant, because it seems a direct response to criticisms by President Trump that the European Union relies too much on NATO and American largess for its defense.

“NATO will always be our collective defense, it’s the strongest military alliance in the world,” Ms. von der Leyen said. “The E.U. will never be a military alliance.” But the European Union can do a lot for its defense outside NATO, including standardizing how it chooses and researches defense systems.

Ms. von der Leyen has supported the idea of a European Union army in the past, a vision she’s shelving for now.

Managing migration becomes a ‘way of life.’

When Ms. von der Leyen announced that Greek-born Brussels veteran Margaritis Schinas would become vice president of the commission for “Protecting Our European Way of Life,” there were puzzled faces across the press room.

This will include, she said, investing in countries where migrants come from, so more opportunities are available for them there; finding ways to create “humane, effective and functioning external borders,” to stop undocumented migrants and asylum seekers; and ensuring that the European Union can continue the “noble task” of accepting refugees “in a way that is orderly and regular.”

One critical way the European Union has managed migration over the past five years, in a bid to stop thousands from arriving at its shores, has been paying Turkey and other countries to keep migrants away. Asked if she would renew the Turkey deal, which has cost the European Union taxpayer 6 billion euros (about $6.6 billion), especially after noting that Turkey didn’t share European Union values at another point in her presentation, Ms. von der Leyen sidestepped. “We will see,” she said.

Ms. von der Leyen wants Brexit to be a ‘new start’

Ms. von der Leyen tried to put a positive spin on Brexit but acknowledged Britain’s impending departure from the European Union would be hard.

“Brexit, should it happen, is not the end of something but it’s the beginning of our future relationship,” she said.

One issue that will affect her directly is that, should London ask for an extension to the Oct. 31 deadline for its withdrawal — and should the remaining 27 European Union member states decide to grant it — she would be legally obliged to ask Britain to send a commissioner to Brussels.

More immediately, and perhaps more consequentially, Ms. von der Leyen appointed an Irishman, Phil Hogan, to be commissioner for trade. Irish-British relations are especially fraught at the moment with the border between the two countries being the main sticking point in Brexit.

Mr. Hogan would be tasked with negotiating a new trade deal between the European Union and Britain after Brexit, one of the most important elements of the future relationship between the two.